Topology-based Methods for Analysis and Visualization of Noisy Data

基于拓扑学的噪声数据分析和可视化方法主要研究人员：Bernd Hamann，加州大学戴维斯分校摘要由不断发展的超级计算机、大型传感器网络和高分辨率成像设备生成的科学数据集的大小正在以指数速度快速增长。该项目解决了对更有效的数据分析方法的需求。它开发了与非常大的科学数据集的分析和表示有关的技术，强调捕捉定性特征的概念。鉴于直接应用于“原始”科学数据集的纯粹基于可视化的方法的局限性，该项目旨在设计用于可视化非常大和复杂的数据集的新概念。正在开发的方法首先从给定的数据集中提取有意义的定性信息，然后使用这些信息以明显更紧凑的形式呈现数据集的更高级别的信息内容，从而强调相关的定性行为。该项目建立在经典拓扑和几何的概念基础上，这两个概念对计算拓扑和计算几何相对较新的领域的发展做出了重大贡献。这两个领域拥有巨大的潜力，可以大幅推进可视化技术，以理解极大的、复杂的数据集。该项目将用于平滑数学函数的计算拓扑和计算几何算法适配(并推广)到真实世界的有限样本数据集，即在有限数量的点上采样的函数(可能通过网格连接)。真实世界的数据集是有噪声的，这使得最初为光滑函数开发的拓扑方法的应用变得更加复杂。这个项目研究了基于Morse和Morse-Smer理论(研究临界点行为并得出关于函数的定性结论)的技术到随时间变化且也包含噪声的离散化标量场的技术推广。

Topology-based Methods for Analysis and Visualization of Noisy DataPrincipal Investigator: Bernd Hamann, University of California, DavisAbstractThe size of scientific data sets that are generated by evolving supercomputers, large sensor networks, and high-resolution imaging devices is increasing rapidly, at an exponential rate. This project addresses the need for more effective data analysis methods. It develops technologies concerned with the analysis and representation of very large scientific data sets, emphasizing concepts that capture qualitative characteristics. In light of the limitations of purely visualization-based approaches applied to "raw" scientific data sets directly, this project aims at devising new concepts for visualizing very large and complex data sets. The methods being developed first extract meaningful qualitative information from a given data set, which is then used to present the higher-level information content of the data set in a significantly more compact form, thus stressing relevant qualitative behavior.The project builds on concepts from classical topology and geometry, which have contributed substantially to the development of the relatively new fields of computational topology and computational geometry. These two fields hold great potential for substantially advancing the visualization technology for understanding extremely large, complicated data sets. This projects adapts (and generalizes) computational topology and computational geometry algorithms that are well-established for smooth mathematical functions to real-world, finite-sample data sets, i.e., functions sampled at a finite number of points (that could possibly be connected by a mesh). Real-world data sets are noisy, which further complicates the application of topological methods that were developed originally for smooth functions. This project investigates the generalization of techniques based on Morse and Morse-Smale theory (studying critical-point behavior and drawing qualitative conclusions about functions) to discretized scalar fields that change over time and also contain noise.